## anonymous one year ago 5th root (-3)^5 ._.

1. kropot72

It can be written as the power of a power: $\large \sqrt[5]{(-3)^{5}}=((-3)^{5})^\frac{1}{5}$

2. kropot72

Just multiply the indices (5 * (1/5).

3. misty1212

HI!!

4. misty1212

the fifth root of whatever to the power of five is whatever

5. misty1212

$\huge \sqrt[5]{\diamondsuit^5}=\diamondsuit$

6. anonymous

So if it's the same number it's going to be whatever the inside number is? (I have no clue if that made sense)

7. anonymous

@misty1212 Do you think you could help me with another problem?

8. misty1212

sure

9. misty1212

and yes, it is the same number that is inside, so your answer should be $$-3$$

10. anonymous

Cool, um, my next question is a 5th root of -1/32

11. anonymous

I don't understand fractions all that well and since I'm new to this whole 5th root, I'm extremely confused about it.

12. misty1212

your job is to think of a number that, when raised to the fifth power, is 32

13. misty1212

don't think too hard , it is easy to come by that is not the final answer btw, but that is the first step

14. misty1212

if you do not get it, let me know if you do, say it

15. anonymous

So it'd just be multiplying something by itself to get to 32?

16. misty1212

yes one number, multiplied by itself five times, to give 32

17. misty1212

i will be happy to tell you if you like

18. anonymous

Would it be 2? and since it's a negative 32, the answer would be -2?

19. misty1212

yes $$2^5=32$$ so $$\sqrt[5]{32}=2$$ but as i said, we are still not done

20. misty1212

you want $\sqrt{-\frac{1}{32}}$ which is the same as $\frac{\sqrt[5] 1}{\sqrt[5]{-32}}$

21. misty1212

$\sqrt[5]{1}=1$ and $\sqrt[5]{-32}=-2$

22. anonymous

So would it be the 5th root 1 over -2?

23. misty1212

no it would just be $-\frac{1}{2}$

24. misty1212

not the fifth root, you already took the fifth root

25. anonymous

Ohhh, I see now.

26. misty1212

ok good !!

27. anonymous

Thank you! :)

28. misty1212

$\huge \color\magenta\heartsuit$